The Ton moved top of the Irn-Bru First Division for the first time this season as they fought back from a goal down against Jim Jefferies' side to complete a remarkable week that had them beat Partick Thistle 2-1 on Boxing Day.
A Michael Tidser double and strikes from Fouad Bachirou and Peter Weatherson were enough to see off the Pars, who took the lead when Callum Morris netted and pulled it back to 3-2 through Ryan Wallace.
Moore said: "That performance is up there with the best since I came to Morton.
"And to come back from 1-0 down against a team like Dunfermline is a big ask. But the boys have belief about them.
"I am delighted to see Tidser score a couple and for wee Freddie Bachirou to score as well is brilliant – although it may take until next year to get another from him.
"But it is a great win and to go top as well while never being up there says a lot."
A crowd of 3,076 watched the promotion clash as Moore's side moved top of the table, but Cappielow chief Douglas Rae has warned a return to part-time football could be on the cards if fans don't turn up in their numbers.
Writing in Saturday's match programme, chairman Rae explained: "Our club is experiencing worrying deficits every week at present.
"Our Second Division average attendance was 2,808. This season our average attendance has shrunk to below 1,400 which frankly makes it impossible for us to be a full-time team.
"In fact there is not a team in the SFL that can currently afford to be full-time."
Elsewhere, Ian Murray is confident Dumbarton can push on after sealing his first win in charge with a 4-3 win at Falkirk.
He said: "We knew we had that in our locker – that is why losing to Hamilton was so disappointing, but maybe we needed it to get the cobwebs away. As a group we really do work hard."
Meanwhile, Albion Rovers boss Todd Lumsden has hit out at referee John Beaton after a controversial penalty call denied them a point at Arbroath.
The Coatbridge side were heading for a draw at Gayfield as Ciaran Donnelly cancelled out Derek Holmes' opener for the hosts, but Steven Doris converted from the spot after Beaton ruled Donnelly had handled inside the area.
Lumsden said: "I fail to see how the referee could give a penalty with the players so close to each other – that has cost us. The ref seemed desperate to give Arbroath a penalty."
In the Third Division, Jim Duffy criticised the Clyde fans as his side claimed all three points against Berwick, with goals from Dougie Brydon and Kevin Watt.
Duffy said: "We were second best in the first half, but games last 90 minutes. I'm delighted.
"I wasn't impressed with the criticism from fans at half-time. This was an inexperienced side who came back with a fine win days after facing Rangers."